Having a bunch of problems with the questions premise. The Tlingit people were composed of several smaller tribes and coordinated frequently with the Haida people in raids along the coast (the Salish and Qualicum tribes were frequent targets), but these raids were further south into what is now Vancouver and Puget sound.
But the part that I'm having troubles with is the suggestion that these tribes were subjugated by Russian interests. For starters, I can't find a single reference that the Haida peoples decline was due to subjugation by the Russians in any manner. The Haida, like most other native tribes, suffered heavily from European disease (most notably small pox). Much of Haida culture/history was stored upon Totems, however Christians found these to be graven images and would dismantle them or move them off to museums and collectors. The final hit to the Haida culture came from the Canadians in the form of residential schools (many Haida children were sent to residential schools around 1911 inland as far as Alberta where they were assimilated into western culture).
The Kwakiutl people underwent a similar fate, being on Vancouver island they fell heavily to disease followed by residential schools and the dismantling of their culture to integrate with Western culture. This was a constant fate of most tribes in the British controlled regions surrounding Vancouver, but they fall well outside of "than other groups more completely subjugated by the Russians" as these groups were never really subjugated by the Russians and their decline directly relates to the British/Americans.
Aluutiq are a notable exception to the tribes above as they were flat out slaughtered by the newly arriving Russians. They were considerably less militaristic than the Tlingit or Haida people, so there is something to say about the Tlingits ability to resist.
To the Tlingits...they were often compared to Vikings in culture and way of life. Trade was heavily involved (hence why small pox hit them so hard), but they were frequently documented in raiding parties slaughtering other native tribes or attacking Americans as far south as what would become Seattle. Their raids on Russian interests definitely hindered the Russians as well, but they appeared to be willing to raid/attack any people nearby, not just Russians
From the Haida people wiki page https://en.wikipedia.org/wiki/Haida_people :
When the Haida and Tongass (sea lion tribe Tlingit) warriors refused to acknowledge American jurisdiction and to hand over those among them who had attacked the Puget Sound communities, a battle ensued in which 26 natives and one government soldier were killed. In the aftermath of this, Colonel Isaac Ebey, a US military officer and the first settler on Whidbey Island, was shot and beheaded on 11 August 1857 by a small Tlingit group from Kake, Alaska, in retaliation for the killing of a respected Kake chief in the raid the year before.
This militaristic nature may have staved off the Russian slaughter that befell the Aluutiq people, but the major reason their culture has endured has more to due with Geography and the British/Canadian peoples...they lived further north into area's the residential schooling policies were never enacted as opposed to the many tribes further south that got caught up in residential schools.
This might be a living answer as it'll be updated as I find more information.